NTA JEE Mains 05th April 2024 Shift 2

A particle moves in $$x - y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\vec{p}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$$. If $$k$$ is constant, the angle between $$\vec{F}$$ and $$\vec{p}$$ will be :

What is the dimensional formula of $$ab^{-1}$$ in the equation $$\left(P + \frac{a}{V^2}\right)(V - b) = RT$$, where letters have their usual meaning.

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $$9$$ m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$m/s^2$$) :

A heavy box of mass $$50$$ kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $$t$$ is proportional to :

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : (Given = Radius of geo-stationary orbit for earth is $$4.2 \times 10^4$$ km)

Match List-I with List-II :

Choose the correct answer from the options given below :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $$\frac{C_P}{C_V}$$ for the gas is :

If $$n$$ is the number density and $$d$$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground :